WIX: a wakeness index for preliminary assessment of regional wind farm wake interactions

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Abstract. The rapid clustering of large offshore wind farms in the North Sea and other coastal areas in the world raises concerns about compounded wake losses that propagate for tens of kilometres. Simulating these regional wakes with wind farm parameterisations in numerical weather prediction models is however computationally prohibitive for multi-scenario planning, as each change in layout or turbine specification demands a new simulation. We showcase the Wakeness Index (WIX), a geometry-based indicator that produces rapid, first-order estimates of climatological wake footprints from only three inputs: turbine coordinates and rotor diameters, wind direction frequency statistics, and a single tuneable decay factor df. The WIX is here calibrated against year-long simulations using the Weather Research and Forecasting (WRF) model with the Fitch wind farm parameterisation for current, and projected 2030 and 2050 North Sea scenarios, using the footprints' intersection-over-union (IoU) at the 92, 95, and 98 % wind speed recovery levels and the pixel-wise coefficient of determination R2 for the velocity deficit field. The footprint optimum over all scenarios (df = 2.3, mean IoU = 0.75) is adopted as the operating point. The future, higher-density layouts are reproduced skilfully and share common optima (IoU up to 0.87, R2 up to 0.92), demonstrating generalisability across comparable turbine populations. The WIX transfers to the more stable regime of the Baltic Sea without region-specific tuning, and wind direction frequencies from the New European Wind Atlas (NEWA) dataset can substitute the WRF-derived wind direction frequency statistics with near-perfect agreement, removing the dependency on output from localized simulations. Computing the WIX over the entire North Sea is reduced to a few seconds on 32 CPUs, against the CPU-weeks required by the WRF model, the WIX is well suited as a lightweight pre-feasibility screening tool for early-stage wind farm and marine spatial planning.

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